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José N. Contreras

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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Enrique Ortiz

This article includes an original artwork using geometry. Art such as this can foster understanding and appreciation of fundamental concepts across fields.

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Priya V. Prasad

Assess the robustness of students’ understanding of polygons and move students beyond drawing to constructing geometric shapes.

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Courtney R. Nagle and Deborah Moore-Russo

Students must be able to relate many representations of slope to form an integrated understanding of the concept.

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Kyle T. Schultz and Stephen F. Bismarck

A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.

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Sonali Raje, Michael Krach, and Gail Kaplan

Stereochemistry and three-dimensional analysis constitute significant parts of this student activity.

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S. Asli Özgün-Koca, Michael Todd Edwards, and Michael Meagher

The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.

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Kimberly M. Lilienthal

Exploring airport traffic, usage, hours of operation, and security statistics are all ways to model and bring relevance to math. Students soar while exploring the mathematics of aircraft: dimensions, cargo, fuel, and passenger capacity. Comparing two airports or aircraft would be valuable ways to extend their mathematical journey.

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Christopher E. Smith

Considering circles in taxicab geometry helps students with Euclidean concepts.

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Emily Sliman

Chalk Talk and Claim-Support-Question are two routines for developing students' ability to use multiple representations and encouraging classroom discussion.